Download or read book Development of a Time Domain Hybrid Finite Difference finite Element Method for Solutions to Maxwell s Equations in Anisotropic Media written by Christopher W. Kung and published by . This book was released on 2009 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: The finite difference time domain (FDTD) and finite element numerical methods are two popular time domain computational methods in electromagnetics, but the two numerical methods have certain tradeoffs. FDTD is a fast explicit method with second order accuracy, but the method's accuracy is reduced when analyzing structures that are not conforming to a Cartesian grid. The finite element method on the other hand excels at examining domains with non-conforming structures, but its method of solution usually requires a matrix inverse operation, which is computationally expensive. Fortunately, research in hybrid methods have shown that the FDTD method for isotropic materials can be viewed upon as a subset of finite elements, and from this viewpoint, the FDTD and finite element method in the time domain can be hybridized together to the advantages of both methods while mitigating the disadvantages.

Download or read book Time Domain Finite Element Methods for Maxwell s Equations in Metamaterials written by Jichun Li and published by Springer Science & Business Media. This book was released on 2012-12-15 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to provide an up-to-date introduction to the time-domain finite element methods for Maxwell’s equations involving metamaterials. Since the first successful construction of a metamaterial with both negative permittivity and permeability in 2000, the study of metamaterials has attracted significant attention from researchers across many disciplines. Thanks to enormous efforts on the part of engineers and physicists, metamaterials present great potential applications in antenna and radar design, sub-wavelength imaging, and invisibility cloak design. Hence the efficient simulation of electromagnetic phenomena in metamaterials has become a very important issue and is the subject of this book, in which various metamaterial modeling equations are introduced and justified mathematically. The development and practical implementation of edge finite element methods for metamaterial Maxwell’s equations are the main focus of the book. The book finishes with some interesting simulations such as backward wave propagation and time-domain cloaking with metamaterials.

Download or read book Development and Evaluation of Novel Finite difference Time domain Methods for Solving Maxwell s Equations written by Guilin Sun and published by . This book was released on 2004 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Element Time Domain Techniques for Maxwell s Equations Based on Differential Forms written by Joonshik Kim and published by . This book was released on 2010 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: This dissertation is concerned with the development of numerical techniques for solving Maxwell equations in the time-domain. Two of the main challenges to obtain such solution are, first, how to construct explicit (that is, matrix-free) time-updating formulas without relinquishing the advantage of using irregular unstructured meshes in complex geometries, and second, how to best parallelize the algorithm to solve large-scale problems. The finite element time-domain (FETD) and the finite-difference time-Domain (FDTD) are presently the two most popular methods for solving Maxwell equations in the time-domain. FDTD employs a staggered-grid spatial discretization together with leap-frog style time update scheme to produce a method with many desirable properties such as: conservation of charge and energy, absence of spurious mode, and a simple easy-to-code algorithm. Nevertheless, FDTD (in its conventional form) relies on orthogonal grids, which is a disadvantage when modeling complex geometries. On the other hand, FETD is based upon unstructured grids and hence naturally tailored to handle complex geometries. However, in time-domain simulation (as opposed to frequency-domain simulations), FETD requires a matrix solver at every time step. Since the total number of time steps to produce the overall time-domain solution can be quite large, this requirement demands excessive computational resources. To overcome this problem, we develop a FETD algorithm with "FDTD-like" explicit characteristics. Usually, the system matrices generated after discretizing Maxwell equations in irregular grids are very large and sparse matrices, while their inverses are very large and dense matrices. To construct an explicit algorithm, ideally one would need to somehow obtain and use such inverses. However, these dense matrices are of course not useful in a update scheme because they are not only very costly to compute but also very costly to store for most practical problems. For this reason, we investigate the use of approximate sparse inverses to build update schemes for FETD. We show that the most direct choice, which is to use the approximate inverse of the system matrix itself, is not really an adequate choice because of the nature of the corresponding (continuum) operator, with long-range interactions. We therefore consider instead the use of the approximate inverse of the Hodge (or mass) matrix, which a symmetric positive definite matrix representing a strictly local operator in the continuum limit whose inverse is also local, to compute explicit update schemes. This entails the discretization of Maxwell's equations based on discrete differential forms and the use of a "mixed" set of basis functions for the FETD: Whitney one forms for the electric field intensity and Whitney two forms for the magnetic flux density. This choice of basis functions obeys a discrete version of the de Rham diagram and leads to solutions that are free of spurious modes and numerically stable. We construct a parallel approach to compute the approximate inverse, and provide an error analysis of the resulting solutions versus the density of the approximate inverse and the mesh refinement considered. A higher-order version of the mixed FETD algorithm is also constructed, showing good convergence versus the polynomial order.

Download or read book Finite Element Methods for Maxwell s Equations written by Peter Monk and published by Oxford University Press. This book was released on 2003-04-17 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Methods For Maxwell's Equations is the first book to present the use of finite elements to analyse Maxwell's equations. This book is part of the Numerical Analysis and Scientific Computation Series.

Download or read book Finite difference Time domain Solutions to Maxwell s Equations Including Interactions with Lumped Elements Charged particle Fluids and Gain Media written by Wenquan Sui and published by . This book was released on 1997 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Least Squares Finite Element Method written by Bo-nan Jiang and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first monograph on the subject, providing a comprehensive introduction to the LSFEM method for numerical solution of PDEs. LSFEM is simple, efficient and robust, and can solve a wide range of problems in fluid dynamics and electromagnetics.

Download or read book Automated Solution of Differential Equations by the Finite Element Method written by Anders Logg and published by Springer Science & Business Media. This book was released on 2012-02-24 with total page 723 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.

Download or read book Space Antenna Handbook written by William A. Imbriale and published by John Wiley & Sons. This book was released on 2012-06-25 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses a broad range of topics on antennas for space applications. First, it introduces the fundamental methodologies of space antenna design, modelling and analysis as well as the state-of-the-art and anticipated future technological developments. Each of the topics discussed are specialized and contextualized to the space sector. Furthermore, case studies are also provided to demonstrate the design and implementation of antennas in actual applications. Second, the authors present a detailed review of antenna designs for some popular applications such as satellite communications, space-borne synthetic aperture radar (SAR), Global Navigation Satellite Systems (GNSS) receivers, science instruments, radio astronomy, small satellites, and deep-space applications. Finally it presents the reader with a comprehensive path from space antenna development basics to specific individual applications. Key Features: Presents a detailed review of antenna designs for applications such as satellite communications, space-borne SAR, GNSS receivers, science instruments, small satellites, radio astronomy, deep-space applications Addresses the space antenna development from different angles, including electromagnetic, thermal and mechanical design strategies required for space qualification Includes numerous case studies to demonstrate how to design and implement antennas in practical scenarios Offers both an introduction for students in the field and an in-depth reference for antenna engineers who develop space antennas This book serves as an excellent reference for researchers, professionals and graduate students in the fields of antennas and propagation, electromagnetics, RF/microwave/millimetrewave systems, satellite communications, radars, satellite remote sensing, satellite navigation and spacecraft system engineering, It also aids engineers technical managers and professionals working on antenna and RF designs. Marketing and business people in satellites, wireless, and electronics area who want to acquire a basic understanding of the technology will also find this book of interest.

Download or read book Time Domain Simulation of Maxwell s Equations by the Method of Characteristics written by Neven Orhanović and published by . This book was released on 1993 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: A numerical method based on the the method of characteristics for hyperbolic systems of partial differential equations in four independent variables is developed and used for solving time domain Maxwell's equations. The method uses the characteristic hypersurfaces and the characteristic conditions to derive a set of independent equations relating the electric and magnetic field components on these hypersurfaces. A discretization scheme is developed to solve for the unknown field components at each time step. The method retains many of the good features of the original method of characteristics for hyperbolic systems in two independent variables, such as optimal time step, good behavior near data discontinuities and the ability to treat general boundary conditions. The method is exemplified by calculating the time domain response of a few typical planar interconnect structures to Gaussian and unit step excitations. Although the general emphasis is on interconnect problems, the method is applicable to a number of other transient electromagnetic field problems governed by Maxwell's equations. In addition to the method of characteristics a finite difference scheme, known in mathematic circles as the modified Richtmyer scheme, is applied to the time domain solution of Maxwell's equations. Both methods should be useful for efficient full wave analysis of three dimensional electromagnetic field problems.

Download or read book A Two dimensional Finite difference Time domain Solution of Maxwell s Equations in Inhomogeneous Media written by Scott Robert Vechinski and published by . This book was released on 1986 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Accurate Finite difference Scheme and Finite element Method for some Partial Differential Equations written by Ulziibayar Vandondoo and published by Springer. This book was released on 2023-11-20 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is intended for graduate students, researchers and teachers. It is devoted to the construction of high-order schemes of the finite difference method and the finite element method for the solution of multidimensional boundary value problems for various partial differential equations, in particular, linear Helmholtz and wave equations, and nonlinear Burgers' equation. The finite difference method is a standard numerical method for solving boundary value problems. Recently, considerable attention has been paid to constructing an accurate (or exact) difference approximation for some ordinary and partial differential equations. An exact finite difference method is developed for Helmholtz and wave equations with general boundary conditions (including initial condition for wave equation) on the rectangular domain in R2. The method proposed here comes from [4] and is based on separation of variables method and expansion of one-dimensional three-point difference operators for sufficiently smooth solution. The efficiency and accuracy of the method have been tested on several examples.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 836 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Time Domain Finite Difference Computation for Maxwell s Equations written by Jiayuan Fang and published by . This book was released on 1989 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Dual Grid Finite difference Time domain Method for Maxwell Equations in Complex Media written by Jason Cornelius and published by . This book was released on 2019 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A New Finite Difference Time Domain Method to Solve Maxwell s Equations written by and published by . This book was released on 2018 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have constructed a new finite-difference time-domain (FDTD) method in this project. Our new algorithm focuses on the most important and more challenging transverse electric (TE) case. In this case, the electric field is discontinuous across the interface between different dielectric media. We use an electric permittivity that stays as a constant in each medium, and magnetic permittivity that is constant in the whole domain. To handle the interface between different media, we introduce new effective permittivities that incorporates electromagnetic fields boundary conditions. That is, across the interface between two different media, the tangential component of the electric field and the normal component of the electric displacement are continuous. Meanwhile, the magnetic field stays as continuous in the whole domain. Our new algorithm is built based upon the integral version of the Maxwell's equations as well as the above continuity conditions. The theoretical analysis shows that the new algorithm can reach second-order convergence O(∆x2)with mesh size ∆x. The subsequent numerical results demonstrate this algorithm is very stable and its convergence order can reach very close to second order, considering accumulation of some unexpected numerical approximation and truncation errors. In fact, our algorithm has clearly demonstrated significant improvement over all related FDTD methods using effective permittivities reported in the literature. Therefore, our new algorithm turns out to be the most effective and stable FDTD method to solve Maxwell's equations involving multiple media.

Download or read book Stability of Finite Element Solutions to Maxwell s Equations in Frequency Domain written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The physics of time-harmonic electromagnetic phenomena can be mathematically described by boundary value problems. A standard approach is based on the vector Helmholtz equation in terms of the electric field. The curl operator involved has a large, non-trivial kernel which leads to an instable solution behaviour at low frequencies. If the boundary value problem is solved approximately using, e. g., the finite element method, the instability expresses itself by a badly conditioned coefficient matrix of the ensuing system of linear equations. A stable formulation is obtained by taking the continuity equation explicitly into account. In order to solve the boundary value problem numerically a finite element software package has been implemented. Its features comprise, amongst others, the treatment of unstructured meshes and piecewise polynomial, anisotropic constitutive parameters as well as the extension of Maxwell's equations to the Perfectly Matched Layer. Successful application of the software is demonstrated with examples from marine geophysics. In particular, the incorporation of seafloor topography by a continuous surface triangulation illustrates the geometric flexibility of the software.